Precalculus Examples

$\frac{{(3 x)}^{3} (2 x)}{36 x^{3}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $2$ and $36$ .

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Step 1.1.1

Factor $2$ out of ${(3 x)}^{3} (2 x)$ .

$\frac{2 ({(3 x)}^{3} (x))}{36 x^{3}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $36 x^{3}$ .

$\frac{2 ({(3 x)}^{3} (x))}{2 (18 x^{3})}$

Step 1.1.2.2

Cancel the common factor.

$\frac{2 ({(3 x)}^{3} (x))}{2 (18 x^{3})}$

Step 1.1.2.3

Rewrite the expression.

$\frac{{(3 x)}^{3} (x)}{18 x^{3}}$

$\frac{{(3 x)}^{3} (x)}{18 x^{3}}$

$\frac{{(3 x)}^{3} (x)}{18 x^{3}}$

Step 1.2

Cancel the common factor of $x$ and $x^{3}$ .

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Step 1.2.1

Factor $x$ out of ${(3 x)}^{3} (x)$ .

$\frac{x {(3 x)}^{3}}{18 x^{3}}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $x$ out of $18 x^{3}$ .

$\frac{x {(3 x)}^{3}}{x (18 x^{2})}$

Step 1.2.2.2

Cancel the common factor.

$\frac{x {(3 x)}^{3}}{x (18 x^{2})}$

Step 1.2.2.3

Rewrite the expression.

$\frac{{(3 x)}^{3}}{18 x^{2}}$

$\frac{{(3 x)}^{3}}{18 x^{2}}$

$\frac{{(3 x)}^{3}}{18 x^{2}}$

$\frac{{(3 x)}^{3}}{18 x^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $3 x$ .

$\frac{3^{3} x^{3}}{18 x^{2}}$

Step 2.2

Raise $3$ to the power of $3$ .

$\frac{27 x^{3}}{18 x^{2}}$

$\frac{27 x^{3}}{18 x^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $27$ and $18$ .

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Step 3.1.1

Factor $9$ out of $27 x^{3}$ .

$\frac{9 (3 x^{3})}{18 x^{2}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $9$ out of $18 x^{2}$ .

$\frac{9 (3 x^{3})}{9 (2 x^{2})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{9 (3 x^{3})}{9 (2 x^{2})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{3 x^{3}}{2 x^{2}}$

$\frac{3 x^{3}}{2 x^{2}}$

$\frac{3 x^{3}}{2 x^{2}}$

Step 3.2

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 3.2.1

Factor $x^{2}$ out of $3 x^{3}$ .

$\frac{x^{2} (3 x)}{2 x^{2}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $x^{2}$ out of $2 x^{2}$ .

$\frac{x^{2} (3 x)}{x^{2} \cdot 2}$

Step 3.2.2.2

Cancel the common factor.

$\frac{x^{2} (3 x)}{x^{2} \cdot 2}$

Step 3.2.2.3

Rewrite the expression.

$\frac{3 x}{2}$

$\frac{3 x}{2}$

$\frac{3 x}{2}$

$\frac{3 x}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$